Diffraction catastrophe

Codimension K

Berry’s unfolding $\varphi \left(s;C\right)$ [18]

Stewart’s unfolding $\varphi \left(x;\Delta \right)$ [19]

Fold

1

$\frac{s^3}{3}+Cs$

$x^3+ax$

Swallowtail

3

$\frac{s^5}{5}+C_3\frac{s^3}{3}+C_2\frac{s^2}{2}+C_{1}s$

$x^5+a{x}^3+b{x}^2+cx$

Wigwam

5

$\frac{s^7}{7}+C_5\frac{s^5}{5}+C_4\frac{s^4}{4}+C_3\frac{s^3}{3}+C_2{s}^2+C_{1}s$

$x^7+a{x}^5+b{x}^4+c{x}^3+d{x}^2+ex$